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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Maths HEP Lunchtime Seminars:

Presented by Pierre Dechant, Durham U

21 February 2014 13:00 in CM221

Clifford algebra often provides a natural geometric interpretation for
algebraic results. We discuss several recent applications of this
framework in the context of Coxeter groups and root systems. For
instance, we show that - unlike the standard approach - it naturally
provides different geometric complex structures for the eigenvalues of
the Coxeter element. Via a construction in terms of Clifford spinors
any 3d root system induces a root system in four dimensions. This
includes all exceptional 4d groups, and as a side effect induces 4d
polytopes and their symmetries from the Platonic solids. The 4d groups
are ubiquitous in HEP, and we explore the connections with Arnold's
trinities and the McKay correspondence. We also discuss affine
extensions of non-crystallographic root systems in a conformal
Clifford approach, as well as some group and representation theoretic

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